One partially ordered set, Q, is a Tukey quotient of another, P – denoted $P{\ge }_{T}Q$ – if there is a map $\varphi :P\to Q$ carrying cofinal sets of P to cofinal sets of Q. Let X be a space and denote by $\mathcal{K}(X)$ the set of compact subsets of X, ordered by inclusion. For certain separable metrizable spaces M, Tukey upper and lower bounds of $\mathcal{K}(M)$ are calculated. Results on invariants of $\mathcal{K}(M)$'s are deduced. The structure of all $\mathcal{K}(M)$'s under ${\le }_T$ is investigated. Particular emphasis is placed on the position of $\mathcal{K}(M)$ when M is: completely metrizable, the rationals $\mathbb{Q}$, co-analytic or analytic.

中文翻译：

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塔基顺序，口径和基本原理

一个部分有序集，Q，是图基商数的另一个，P -表示$P{\ge }_{Ť}问$ –如果有地图 $\varphi ：P\to 问$携带P的最终集合到Q的最终集合。令X为空格并用$\mathcal{ķ}（X）$X的紧凑子集的集合，按包含顺序排序。对于某些可分离的可度量空间M，Tukey的上下界$\mathcal{ķ}（\mathrm{中号}）$计算。的不变量结果$\mathcal{ķ}（\mathrm{中号}）$的推论。所有的结构$\mathcal{ķ}（\mathrm{中号}）$的下 ${\le }_{Ť}$被调查。特别强调的是$\mathcal{ķ}（\mathrm{中号}）$当M为：完全可量化时，有理数$\mathbb{问}$，共同分析或分析。